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N IF
Navigation and Ancillary Information Facility
Dynamic Reference Frames
March 2006
N IF Topics
Navigation and Ancillary Information Facility
• Introduction to Dynamic Reference Frames
• Terminology
• Parameterized Dynamic Reference Frames
• Defining Dynamic Reference Frames
– Two-Vector Frame Concepts
– Two-Vector Frame Examples
– "Of-Date" Frames
– Euler Frames
– Frozen Dynamic Frames
– Inertial Dynamic Frames
• Generic Dynamic Reference Frame Kernel
• Backup
Dynamic Frames 2
N IF Introduction to Dynamic Frames - 1
Navigation and Ancillary Information Facility
• The Dynamic Reference Frames capability is a new
extension to the SPICE Frames system.
– First introduced in the N0058 SPICE Toolkit, released in
January 2005.
• What are "dynamic reference frames"?
– Dynamic reference frames ("dynamic frames" for short)
have time-dependent orientation.
– Dynamic frames are specified via a frame kernel (FK).
– CK and PCK frames are not considered to be dynamic
frames (although they are time-varying).
• The Dynamic Frames capability enables the SPICE
system to conveniently use a wide variety of frames
that are not "built in" to SPICE. Examples include:
– Nadir-oriented frame for planetary orbiter
– Geocentric Solar Ecliptic (GSE)
– Solar Magnetic (SM)
Dynamic Frames 3
N IF Introduction to Dynamic Frames - 2
Navigation and Ancillary Information Facility
– Spacecraft-centered roll-celestial frame
– Geocentric Solar Magnetospheric (GSM)
– Geomagnetic (MAG)
» Using constant north centered geomagnetic dipole
» Using dipole direction defined by time-dependent Euler
angles
– Geocentric Solar Equatorial (GSEQ)
– Solar Equatorial frame for any ephemeris object
– Orbital frame for any ephemeris object
– Earth mean equator and equinox of date
– Earth true equator and equinox of date
– Earth mean ecliptic and equinox of date
– RTN ("radial, tangential, normal") frames
– And many more…
Dynamic Frames 4
N IF Introduction to Dynamic Frames - 3
Navigation and Ancillary Information Facility
• Using dynamic frames in a SPICE-based program is
straightforward:
– At program initialization:
» Load one or more dynamic frame kernels to make
frame definitions known to SPICE.
» Load any kernels on which the dynamic frames
depend.
• Some dynamic frames are defined using data from SPK,
FK, PCK, CK or other SPICE kernels.
– Then, refer to the dynamic frame or frames by name in calls
to SPICE routines:
» Just as you would do with built-in frames such as
J2000.
Dynamic Frames 5
N IF Introduction to Dynamic Frames - 4
Navigation and Ancillary Information Facility
» For example, find the 6x6 matrix to transform states from
the J2000 frame to the Geocentric Solar Ecliptic (GSE)
frame at the TDB epoch given by ET.
CALL SXFORM( 'J2000', 'GSE', ET, XFORM )
» Or look up the state of Jupiter relative to the earth in the
GSE frame:
CALL SPKEZR( 'JUPITER', ET, 'GSE',
'NONE', 'EARTH', STATE, LT )
• You can refer to dynamic frames in SPK or CK files,
for example:
– When you create an SPK file, you can have an SPK segment
reference its ephemeris data to the true earth equator and
equinox of date reference frame.
» However, some restrictions apply to use of dynamic
frames in SPICE kernels (see Backup slides).
Dynamic Frames 6
N IF Introduction to Dynamic Frames - 5
Navigation and Ancillary Information Facility
• Defining Dynamic Frames:
– To define dynamic frames via a frame kernel, a fairly
detailed understanding of the SPICE dynamic frame
capability is required.
– A good understanding of the basic SPICE system (in
particular, the SPK and Frame systems) is also a
prerequisite for defining dynamic frames.
– See the Frames Required Reading for the most detailed
documentation available.
– The rest of this tutorial is concerned with
» Explaining the SPICE dynamic frames capability.
» Showing how to create dynamic frame kernels.
• We present many frame definition examples.
Dynamic Frames 7
N IF Terminology - 1
Navigation and Ancillary Information Facility
• Terms involving reference frames and vectors:
– "Frame" is short for "reference frame."
– A frame can be thought of as a set of three mutually
orthogonal, unit-length vectors.
» These vectors are called "basis vectors." The lines
containing the basis vectors are the "axes" of the
frame.
» The basis vectors indicate the "positive" axis
directions; we label these vectors +X, +Y, and +Z. The
negatives of these vectors are labeled -X, -Y, and -Z.
» We number the axes as follows:
X = axis 1; Y = axis 2; Z = axis 3
– All of the frames we'll deal with are "right-handed":
equivalently, +Z is the cross product +X x +Y.
– A reference frame's orientation is always defined relative to
another specified frame: the "base frame."
Dynamic Frames 8
N IF Terminology - 2
Navigation and Ancillary Information Facility
– When we say that a frame is "time-dependent" or "time-
varying," we mean:
» The orientation of the frame is time-dependent.
» Equivalently, the rotation between the frame and its
base frame is time-dependent.
– By "evaluating" a frame or "evaluating the orientation of a
frame," we mean computing the rotation between the frame
and its base frame.
» An epoch is required in order to evaluate a dynamic
frame.
– In the SPICE system, frames are considered to have
"centers."
» The center of a frame is always an ephemeris object.
» Frame centers come into play when light time
corrections are used: the apparent orientation of a
time-dependent frame as seen by an observer is
affected by the one-way light time between the frame's
center and the observer.
Dynamic Frames 9
N IF Terminology - 3
Navigation and Ancillary Information Facility
– When we say that a vector is "aligned" with another vector,
we mean that the angular separation between the two
vectors is zero.
– We use the terms "defining a frame" and "specifying a
frame" interchangeably. Both refer to creating a frame
definition in a frame kernel.
• Other definitions:
– The term "API" stands for "Application Programming
Interface." This term refers to the set of SPICE routines
that are intended to be called directly by SPICE-based
programs.
– The notation
[theta]n
indicates a frame rotation of theta radians about axis n,
where n is one of {1, 2, 3}. This transformation rotates
vectors by –theta radians about axis n.
Dynamic Frames 10
N IF Parameterized Dynamic Frames - 1
Navigation and Ancillary Information Facility
• Parameterized dynamic frames
– This is the only frame definition style currently supported by
the dynamic frame system.
» Future versions of SPICE might support additional styles.
– Frames are defined via parameterized formulas
» The code implementing the formulas themselves is built
into SPICE.
» The parameters are specified in a frame kernel.
– Parameterized dynamic frames are grouped into frame
"families". Each family corresponds to a distinct,
parameterized geometric formula providing a frame
definition. The families are:
» Two-Vector Frames
» Mean Equator and Equinox of Date Frames
» True Equator and Equinox of Date Frames
» Mean Ecliptic and Equinox of Date Frames
» Euler Frames
Dynamic Frames 11
N IF Parameterized Dynamic Frames - 2
Navigation and Ancillary Information Facility
• Defining Parameterized Dynamic Frames
– Parameterized Dynamic frames are defined using
"keyword=value" assignments in a frame kernel. The
following items must be specified in the frame definition:
» Frame name
» Frame ID code
• The range 1400000-2000000 is reserved for SPICE users
» Class (=5 for dynamic frames)
» Class ID code (=frame ID code for dynamic frames)
» Frame center (=NAIF ID code for central body)
» Frame definition style (='PARAMETERIZED')
» Base frame
• Frame definition specifies mapping from dynamic
frame to the base frame.
» Frame family
» Family-specific assignments
Dynamic Frames 12
N IF Parameterized Dynamic Frames - 3
Navigation and Ancillary Information Facility
» Rotation state
• Possible states are 'ROTATING' and 'INERTIAL'.
– Frame is treated as rotating or inertial for the purpose
of velocity transformations.
• The default dynamic frame rotation state is 'ROTATING'.
• For rotating two-vector and Euler frames, the rotation state
assignment can be omitted from the frame definition.
• For "of-date" frames, the frame definition must either
specify the rotation state or designate the frame as
"frozen" at a specified epoch.
» Freeze epoch.
• Presence of this optional assignment in a frame kernel
indicates that the frame orientation, relative to the base
frame, is held constant ("frozen") at the specified epoch.
• Most dynamic frames are not frozen.
Dynamic Frames 13
N IF Two-Vector Frame Concepts - 1
Navigation and Ancillary Information Facility
• Two-vector frames are defined using two time-
dependent vectors: the "primary" and
"secondary" vectors.
– Each of the primary and secondary vectors may be defined by
a variety of geometric means. Each vector may be a
» Position vector
» Target near point vector
» Velocity vector
» Constant vector
• The user associates specified positive or
negative axes of the two-vector frame with the
primary and secondary vectors.
– Two-vector frames are always right-handed and have
orthogonal axes, so two non-parallel vectors and associations
of axes with these vectors suffice to define the orientation of a
frame.
Dynamic Frames 14
N IF Two-Vector Frame Concepts - 2
Navigation and Ancillary Information Facility
• Primary Vector
– A specified positive or negative axis of the two-vector
frame is aligned with this vector.
» The frame kernel creator assigns to this vector one of
the axis designations { +X, -X, +Y, -Y, +Z, -Z }.
– Two degrees of freedom of the frame orientation are
removed by association of an axis with the primary vector.
The third degree of freedom is the frame's rotation about
the primary vector.
– Example: a frame's -X axis is aligned with the primary
vector:
Y
-X
Primary Vector
Z
X
Dynamic Frames 15
N IF Two-Vector Frame Concepts - 3
Navigation and Ancillary Information Facility
• Secondary Vector
– A specified positive or negative axis of the two-vector frame is
aligned with the component of the secondary vector
orthogonal to the primary vector.
» The frame kernel creator associates with this vector one of
the axis designations { +X, -X, +Y, -Y, +Z, -Z }, where the
axis is orthogonal to that associated with the primary
vector.
– Example, continued: the frame's +Y axis is associated with the
secondary vector. The component of the secondary vector
orthogonal to the primary vector is aligned with the frame's +Y
axis. The secondary vector thus lies in the frame's X-Y plane.
-X Y
Primary Vector
Secondary Vector
Z
Component of secondary
X vector orthogonal to primary
vector
Dynamic Frames 16
N IF Two-Vector Frame Concepts - 4
Navigation and Ancillary Information Facility
• Secondary Vector, continued
– Typically the secondary vector itself is not orthogonal to the
primary vector.
– The secondary vector must be linearly independent of the
primary vector.
» Near-degenerate geometry can lead to extreme loss of precision.
• This problem can be difficult to diagnose.
» SPICE enforces independence using a default angular separation
tolerance of 1 milliradian. The angular separation of the primary
and secondary vectors may not differ from 0 or Pi radians by less
than this tolerance.
» A frame kernel creator can specify a different tolerance value.
The frame kernel assignment for this is:
FRAME_<frame_ID>_ANGLE_SEP_TOL = <tolerance>
where the tolerance is given in radians.
– Designers of two-vector frames should ensure that the primary
and secondary vectors can't become nearly parallel for any
realistic evaluation epoch.
Dynamic Frames 17
N IF Two-Vector Frame Concepts - 5
Navigation and Ancillary Information Facility
• Position Vector
– Is defined by the position of one ephemeris object relative
to another. The frame kernel creator specifies:
» the target
» the observer
» the aberration correction
• The vector may optionally be corrected for light time and
stellar aberration.
– The epoch at which the position vector is computed is
supplied via a call to a SPICE API routine:
» as an input to an SPK routine, e.g. SPKEZR, SPKPOS.
» as an input to a frame system routine, e.g. SXFORM,
PXFORM.
– The reference frame relative to which the vector is
expressed is not specified by the frame kernel creator.
» SPICE automatically selects this frame.
Dynamic Frames 18
N IF Two-Vector Frame Concepts - 6
Navigation and Ancillary Information Facility
• Target Near Point Vector
– Is defined as the vector from an observer to the nearest point
on a specified extended target body to that observer. The frame
kernel creator specifies:
» the target
» the observer
» the aberration correction
• The vector may optionally be corrected for light time and
stellar aberration.
• When light time correction is used, both the position and
orientation of the target body are corrected for light time.
– The extended target body is modeled as a triaxial ellipsoid.
» Size and shape data are given by a PCK.
– The epoch is supplied via a SPICE API call, as for position
vectors.
– The reference frame relative to which the vector is expressed is
not specified by the frame kernel creator.
» SPICE automatically selects this frame.
Dynamic Frames 19
N IF Two-Vector Frame Concepts - 7
Navigation and Ancillary Information Facility
• Velocity Vector
– Is defined by the velocity of a target ephemeris object relative
to an observing ephemeris object. The frame kernel creator
specifies:
» the target
» the observer
» the velocity reference frame
• This frame may be distinct from the base frame.
• Different velocity frame choices can lead to radically different
two-vector frame definitions.
» the aberration correction
• The velocity vector may optionally be corrected for light time
and stellar aberration.
• Use of light time correction also implies evaluation of the
velocity vector's frame at a light-time corrected epoch: the
epoch is corrected for light time between the velocity frame's
center and the observer, if the velocity frame is non-inertial.
– The epoch is supplied via a SPICE API call, as for position
vectors.
Dynamic Frames 20
N IF Two-Vector Frame Concepts - 8
Navigation and Ancillary Information Facility
• Constant Vector
– The vector is constant in a frame specified by the kernel
creator.
» The constant vector's frame may be time-dependent.
» This frame may be distinct from the base frame.
– The vector may be specified in a variety of coordinate
systems.
» Cartesian
» Latitudinal
» Right ascension/declination (RA/DEC)
– An observer may optionally be associated with a constant
vector for the purpose of defining aberration corrections.
» The orientation of the constant vector's frame may
optionally be corrected for light time between the frame's
center and the observer: if the frame is non-inertial, it is
evaluated at a light-time corrected epoch.
Dynamic Frames 21
N IF Two-Vector Frame Concepts - 9
Navigation and Ancillary Information Facility
» A constant vector may optionally be corrected for
stellar aberration due to motion of observer relative to
solar system barycenter.
• Stellar aberration can be specified without light time
correction; the string indicating stellar aberration
correction alone is
'S'
• This correction specification is not supported elsewhere
in the SPICE Toolkit API.
– The epoch is supplied via a SPICE API call, as for position
vectors.
» If the constant vector's frame is time-dependent, that
frame is evaluated at this epoch, optionally adjusted
for light time.
Dynamic Frames 22
N IF Two-Vector Frame Examples - 1
Navigation and Ancillary Information Facility
Nadir-Oriented Spacecraft-Centered Frame
Primary vector: spacecraft nadir direction
Y = Z x X, completing the vector. Associated with nadir frame's -Z axis in
right-handed frame. frame kernel.
Nadir vector can be
Y defined to point to
either:
• closest point to spacecraft
on ellipsoid
• center of mass of orbited
body
Secondary vector: spacecraft velocity
Z relative to center of motion in J2000
X frame. Associated with nadir frame's
+X axis in frame kernel.
Normalized component of secondary
vector orthogonal to primary vector.
This vector is aligned with the nadir
frame's +X axis.
Dynamic Frames 23
N IF Two-Vector Frame Examples - 2
Navigation and Ancillary Information Facility
Nadir-Oriented Spacecraft-Centered Frame: Frame kernel specification.
The -Z axis points from the spacecraft toward the closest point on Mars.
The component of inertially referenced spacecraft velocity
vector orthogonal to Z is aligned with the +X axis.
The +Y axis is the cross product of the +Z axis and the +X axis.
\begindata <frame_name> = user-specified
frame name
FRAME_<frame_name> = <frame_ID> <frame_ID> = integer frame ID
FRAME_<frame_ID>_NAME = <frame_name> code
FRAME_<frame_ID>_CLASS = 5 <orbiter_ID> = NAIF ID code of
FRAME_<frame_ID>_CLASS_ID = <frame_ID> spacecraft
FRAME_<frame_ID>_CENTER = <orbiter_ID> <orbiter_ID/name> = NAIF ID code or
FRAME_<frame_ID>_RELATIVE = 'J2000' name of spacecraft
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR'
FRAME_<frame_ID>_PRI_AXIS = '-Z'
FRAME_<frame_ID>_PRI_VECTOR_DEF = 'TARGET_NEAR_POINT'
FRAME_<frame_ID>_PRI_OBSERVER = <orbiter_ID/name>
FRAME_<frame_ID>_PRI_TARGET = 'MARS'
FRAME_<frame_ID>_PRI_ABCORR = 'NONE'
FRAME_<frame_ID>_SEC_AXIS = 'X'
FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY'
FRAME_<frame_ID>_SEC_OBSERVER = 'MARS'
FRAME_<frame_ID>_SEC_TARGET = <orbiter_ID/name>
FRAME_<frame_ID>_SEC_ABCORR = 'NONE'
FRAME_<frame_ID>_SEC_FRAME = 'J2000'
Dynamic Frames 24
N IF Two-Vector Frame Examples - 3
Navigation and Ancillary Information Facility
Spacecraft "View Frame"
Secondary vector:
spacecraft position relative to center of motion.
Associated with view frame's +Y axis in frame
X = Y x Z, completing the kernel.
right-handed frame. X
("Out of plane" direction)
Z Primary vector: spacecraft
Y velocity relative to center of
motion in J2000 frame.
Normalized component of secondary
Associated with view frame's
vector orthogonal to primary vector.
+Z axis in frame kernel.
This vector is aligned with the view
("Down track" direction)
frame's +Y axis. ("In plane" direction)
Dynamic Frames 25
N IF Two-Vector Frame Examples - 4
Navigation and Ancillary Information Facility
Spacecraft "View Frame": Frame kernel specification.
The +Z axis is aligned with the J2000-referenced velocity of the
spacecraft relative to Mars.
The component of the spacecraft position orthogonal to +Z is aligned
with the +Y axis.
The +X axis is the cross product of the +Y axis and the +X axis.
\begindata <frame_name> = user-specified
frame name
FRAME_<frame_name> = <frame_ID> <frame_ID> = integer frame ID
FRAME_<frame_ID>_NAME = <frame_name> code
FRAME_<frame_ID>_CLASS = 5 <orbiter_ID> = NAIF ID code of
FRAME_<frame_ID>_CLASS_ID = <frame_ID> spacecraft
FRAME_<frame_ID>_CENTER = <orbiter_ID> <orbiter_ID/name> = NAIF ID code or
FRAME_<frame_ID>_RELATIVE = 'J2000' name of spacecraft
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR'
FRAME_<frame_ID>_PRI_AXIS = 'Z'
FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY'
FRAME_<frame_ID>_PRI_OBSERVER = 'MARS'
FRAME_<frame_ID>_PRI_TARGET = <orbiter_ID/name>
FRAME_<frame_ID>_PRI_ABCORR = 'NONE'
FRAME_<frame_ID>_PRI_FRAME = 'J2000'
FRAME_<frame_ID>_SEC_AXIS = 'Y'
FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_POSITION'
FRAME_<frame_ID>_SEC_OBSERVER = 'MARS'
FRAME_<frame_ID>_SEC_TARGET = <orbiter_ID/name>
FRAME_<frame_ID>_SEC_ABCORR = 'NONE'
Dynamic Frames 26
N IF Two-Vector Frame Examples - 5
Navigation and Ancillary Information Facility
Geocentric Solar Ecliptic Frame (GSE)
Primary vector: position of sun relative to earth
Associated with GSE frame's +X axis in frame kernel.
Z = X x Y,
completing the
right-handed frame
X
Y
Y = normalized component
Secondary vector: velocity of sun of secondary vector
relative to earth in J2000 frame. orthogonal to primary
Associated with GSE frame's +Y axis in vector
frame kernel.
Dynamic Frames 27
N IF Two-Vector Frame Examples - 6
Navigation and Ancillary Information Facility
Geocentric Solar Ecliptic (GSE) frame:
+X is parallel to the geometric earth-sun position vector.
+Y axis is the normalized component of the geometric earth-sun velocity
vector orthogonal to the GSE +X axis.
+Z axis is parallel to the cross product of the GSE +X axis
and the GSE +Y axis.
\begindata
FRAME_GSE = <frame_ID>
FRAME_<frame_ID>_NAME = 'GSE' <frame_ID> = integer frame
FRAME_<frame_ID>_CLASS = 5 ID code
FRAME_<frame_ID>_CLASS_ID = <frame_ID>
FRAME_<frame_ID>_CENTER = 399
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR'
FRAME_<frame_ID>_PRI_AXIS = 'X'
FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION'
FRAME_<frame_ID>_PRI_OBSERVER = 'EARTH'
FRAME_<frame_ID>_PRI_TARGET = 'SUN'
FRAME_<frame_ID>_PRI_ABCORR = 'NONE'
FRAME_<frame_ID>_SEC_AXIS = 'Y'
FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY'
FRAME_<frame_ID>_SEC_OBSERVER = 'EARTH'
FRAME_<frame_ID>_SEC_TARGET = 'SUN'
FRAME_<frame_ID>_SEC_ABCORR = 'NONE'
FRAME_<frame_ID>_SEC_FRAME = 'J2000'
Dynamic Frames 28
N IF Two-Vector Frame Examples - 7
Navigation and Ancillary Information Facility
Geocentric Solar Magnetospheric Frame (GSM)
Secondary vector: North geomagnetic centered
dipole in IAU_EARTH frame. Associated with
GSM frame's +Z axis in frame kernel.
Z = normalized
component of
secondary vector
orthogonal to
primary vector
Primary vector: position of sun relative to earth
Associated with GSM frame's +X axis in frame kernel.
Y = Z x X,
completing the
right-handed frame
Dynamic Frames 29
N IF Two-Vector Frame Examples - 8
Navigation and Ancillary Information Facility
Geocentric Solar Magnetospheric (GSM) frame:
+X is parallel to the geometric earth-sun position vector.
+Z axis is normalized component of north centered geomagnetic dipole
vector orthogonal to GSM +X axis.
+Y completes the right-handed frame.
\begindata
FRAME_GSM = <frame_ID>
FRAME_<frame_ID>_NAME = 'GSM'
FRAME_<frame_ID>_CLASS = 5 <frame_ID> = integer frame
FRAME_<frame_ID>_CLASS_ID = <frame_ID> ID code
FRAME_<frame_ID>_CENTER = 399
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR'
FRAME_<frame_ID>_PRI_AXIS = 'X'
FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION'
FRAME_<frame_ID>_PRI_OBSERVER = 'EARTH'
FRAME_<frame_ID>_PRI_TARGET = 'SUN'
FRAME_<frame_ID>_PRI_ABCORR = 'NONE'
FRAME_<frame_ID>_SEC_AXIS = 'Z'
FRAME_<frame_ID>_SEC_VECTOR_DEF = 'CONSTANT'
FRAME_<frame_ID>_SEC_FRAME = 'IAU_EARTH'
FRAME_<frame_ID>_SEC_SPEC = 'LATITUDINAL'
FRAME_<frame_ID>_SEC_UNITS = 'DEGREES'
FRAME_<frame_ID>_SEC_LONGITUDE = 288.43
FRAME_<frame_ID>_SEC_LATITUDE = 79.54
Dynamic Frames 30
N IF Two-Vector Frame Examples - 9
Navigation and Ancillary Information Facility
Spacecraft-Centered Roll-Celestial Frame
Secondary vector: Lock star direction in J2000 frame, corrected
for stellar aberration due to spacecraft motion. Associated with
Roll-Celestial frame's +X axis in frame kernel.
X = normalized
component of
secondary vector
orthogonal to
primary vector
Primary vector: position of earth relative to spacecraft.
Associated with Roll-Celestial frame's +Z axis
in frame kernel. Y = Z x X,
completing the
right-handed frame
Dynamic Frames 31
N IF Two-Vector Frame Examples - 10
Navigation and Ancillary Information Facility
Spacecraft-centered roll-celestial frame:
+Z is parallel to the geometric earth-sun position vector.
+X axis is normalized component of star direction orthogonal to Z axis. The star
direction is corrected for stellar aberration due to motion of the spacecraft.
+Y completes the right-handed frame.
<frame_name> = user-specified
\begindata frame name
FRAME_<frame_name> = <frame_ID> <frame_ID> = integer frame ID
FRAME_<frame_ID>_NAME = <frame_name> code
FRAME_<frame_ID>_CLASS = 5 <spacecraft_ID> = NAIF ID code of
FRAME_<frame_ID>_CLASS_ID = <frame_ID> spacecraft
FRAME_<frame_ID>_CENTER = <spacecraft_ID> <spacecraft_ID/name> = NAIF ID code or
FRAME_<frame_ID>_RELATIVE = 'J2000' name of spacecraft
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR'
FRAME_<frame_ID>_PRI_AXIS = 'Z'
FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION'
FRAME_<frame_ID>_PRI_OBSERVER = <spacecraft_ID/name>
FRAME_<frame_ID>_PRI_TARGET = 'EARTH'
FRAME_<frame_ID>_PRI_ABCORR = 'NONE'
FRAME_<frame_ID>_SEC_AXIS = 'X'
FRAME_<frame_ID>_SEC_VECTOR_DEF = 'CONSTANT'
FRAME_<frame_ID>_SEC_FRAME = 'J2000'
FRAME_<frame_ID>_SEC_SPEC = 'RA/DEC'
FRAME_<frame_ID>_SEC_UNITS = 'DEGREES'
FRAME_<frame_ID>_SEC_RA = <star right ascension in degrees>
FRAME_<frame_ID>_SEC_DEC = <star declination in degrees>
FRAME_<frame_ID>_SEC_OBSERVER = <spacecraft_ID/name>
FRAME_<frame_ID>_SEC_ABCORR = 'S'
Dynamic Frames 32
N IF "Of-Date" Frames - 1
Navigation and Ancillary Information Facility
• Of-date frames are associated with user-
specified bodies and are based on user-
selected dynamical models.
– Implementations of models are built into SPICE.
• The currently supported "of-date" frame
families are
– Mean Equator and Equinox of Date
– True Equator and Equinox of Date
– Mean Ecliptic and Equinox of Date
• The earth is the only currently supported
body.
Dynamic Frames 33
N IF "Of-Date" Frames - 2
Navigation and Ancillary Information Facility
• The currently supported types of models
are
– Precession
– Nutation
– Mean obliquity
• The of-date frame implementation is
intended to be flexible:
– The set of supported bodies can grow over time.
– The set of supported models can grow over time.
» SPICE is not forever locked into using a
single hard-coded implementation, such as
the 1976 IAU precession model
– The set of supported frame families can grow, if
necessary.
Dynamic Frames 34
N IF "Of-Date" Frames - 3
Navigation and Ancillary Information Facility
• Mean Equator and Equinox of Date Family
– For all reference frames in this family:
» The frame's relationship to the J2000 frame
is given by a precession model.
» The frame kernel creator selects a
precession model from those built into the
SPICE software.
• Currently supported only for the earth
• 1976 IAU precession model (aka Lieske model)
» The frame kernel creator must either specify
the frame's rotation state or must designate
the frame "frozen" at a specified "freeze
epoch."
Dynamic Frames 35
N IF "Of-Date" Frames - 4
Navigation and Ancillary Information Facility
Earth mean equator and equinox of date frame:
+Z axis is perpendicular to mean equator of date and points north.
+X axis is parallel to the cross product of the +Z axis and
the north-pointing vector normal to the mean ecliptic of date.
+Y axis completes the right-handed frame.
\begindata
<frame_name> = user-specified
FRAME_<frame_name> = <frame_ID> frame name
FRAME_<frame_ID>_NAME = <frame_name> <frame_ID> = integer frame ID
FRAME_<frame_ID>_CLASS = 5 code
FRAME_<frame_ID>_CLASS_ID = <frame_ID>
FRAME_<frame_ID>_CENTER = 399
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE'
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
FRAME_<frame_ID>_ROTATION_STATE = 'ROTATING'
Dynamic Frames 36
N IF "Of-Date" Frames - 5
Navigation and Ancillary Information Facility
• True Equator and Equinox of Date Family
– For all reference frames in this family:
» The frame's relationship to the J2000 frame
is given by a precession model and a
nutation model.
» The frame kernel creator selects models
from those built into the SPICE software.
• Currently supported only for the earth
• 1976 IAU precession model (aka Lieske model)
• 1980 IAU nutation model
» The frame kernel creator must either specify
the frame's rotation state or must designate
the frame "frozen" at a specified "freeze
epoch."
Dynamic Frames 37
N IF "Of-Date" Frames - 6
Navigation and Ancillary Information Facility
Earth true equator and equinox of date frame:
+Z axis is perpendicular to true equator of date and points north.
+X axis is parallel to the cross product of the +Z axis and
the north-pointing vector normal to mean ecliptic of date.
+Y axis completes the right-handed frame.
\begindata
<frame_name> = user-specified
FRAME_<frame_name> = <frame_ID> frame name
FRAME_<frame_ID>_NAME = <frame_name> <frame_ID> = integer frame ID
FRAME_<frame_ID>_CLASS = 5 code
FRAME_<frame_ID>_CLASS_ID = <frame_ID>
FRAME_<frame_ID>_CENTER = 399
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE'
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980'
FRAME_<frame_ID>_ROTATION_STATE = 'ROTATING'
Dynamic Frames 38
N IF "Of-Date" Frames - 7
Navigation and Ancillary Information Facility
• Mean Ecliptic and Equinox of Date Family
– For all reference frames in this family:
» The frame's relationship to the J2000 frame
is given by a precession model and an
obliquity model.
» The frame kernel creator selects models
from those built into the SPICE software.
» Currently supported only for the earth
• 1976 IAU precession model (aka Lieske model)
• 1980 IAU mean obliquity model
» The frame kernel creator must either specify
the frame's rotation state or must designate
the frame "frozen" at a specified "freeze
epoch."
Dynamic Frames 39
N IF "Of-Date" Frames - 8
Navigation and Ancillary Information Facility
Earth mean ecliptic and equinox of date frame:
+Z axis is perpendicular to mean ecliptic of date and points toward
ecliptic north.
+X axis is parallel to the cross product of +Z axis and
the north-pointing vector normal to mean ecliptic of date.
+Y axis completes the right-handed frame.
\begindata <frame_name> = user-specified
frame name
FRAME_<frame_name> = <frame_ID> <frame_ID> = integer frame ID
FRAME_<frame_ID>_NAME = <frame_name> code
FRAME_<frame_ID>_CLASS = 5
FRAME_<frame_ID>_CLASS_ID = <frame_ID>
FRAME_<frame_ID>_CENTER = 399
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE'
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980'
FRAME_<frame_ID>_ROTATION_STATE = 'ROTATING'
Dynamic Frames 40
N IF Euler Frames - 1
Navigation and Ancillary Information Facility
• Euler frames are defined by a time-
dependent rotation relative to a base frame.
– The rotation from an Euler frame to its base frame is given
by three Euler angles.
– Each angle is given by a separate polynomial.
» The polynomials may have different degrees.
» The independent variable is a time offset, in TDB
seconds, from an epoch specified by the frame kernel
creator.
» The units associated with the angles are specified by the
frame kernel creator. Angles are converted to radians
internally by SPICE.
» The sequence of rotation axes is specified by the frame
kernel creator.
• The central axis must differ from the other two.
• The rotation from the Euler frame to the base frame is
[angle_1]axis_1 [angle_2]axis_2 [angle_3]axis_3 (units are radians)
Dynamic Frames 41
N IF Euler Frames - 2
Navigation and Ancillary Information Facility
• Examples of applications:
– Dynamic version of earth magnetospheric frame (MAG)
» Latitude and longitude of the north centered geomagnetic
dipole are given by polynomials.
– Spinning spacecraft frame
» The base frame could be a:
• Built-in inertial frame
• C-kernel frame
• Roll-celestial frame (using lock star)
• Nadir frame
– Topocentric frames for tracking stations for which plate
motion is modeled
» The frame rotation keeps the frame orientation consistent
with the changing station location.
Dynamic Frames 42
N IF Euler Frames - 3
Navigation and Ancillary Information Facility
– Mean or true body equator and earth equinox of date
frame, where the body is a planet or satellite other than
the earth
» The base frame is an IAU_<body> frame.
» The Euler frame "removes" the body's rotation about
the spin axis.
– Variation on supported "of date" frame
» An existing supported "of date" frame is used as the
base frame.
» Perturbations to the "of date" frame are expressed
using Euler angles.
Dynamic Frames 43
N IF Euler Frames - 4
Navigation and Ancillary Information Facility
As an example, we construct an Euler frame called IAU_MARS_EULER. Frame
IAU_MARS_EULER is mathematically identical to the PCK frame named IAU_MARS.
The PCK data defining the underlying IAU_MARS frame are:
BODY499_POLE_RA = ( 317.68143 -0.1061 0. )
BODY499_POLE_DEC = ( 52.88650 -0.0609 0. )
BODY499_PM = ( 176.630 350.89198226 0. )
Relative to the angles used to define the IAU_MARS frame, the angles for our
Euler frame definition are reversed and the signs negated. Angular units are
degrees. Rate units are degrees/second, unlike the PCK units of degrees/day.
angle_3 is 90 + RA angle_1 is -90 - RA
PCK: angle_2 is 90 - Dec Euler Frame: angle_2 is -90 + Dec
angle_1 is PM angle_3 is - PM
\begindata
FRAME_IAU_MARS_EULER = <frame_ID>
FRAME_<frame_ID>_NAME = 'IAU_MARS_EULER'
FRAME_<frame_ID>_CLASS = 5 <frame_ID> = integer frame ID
FRAME_<frame_ID>_CLASS_ID = <frame_ID> code
FRAME_<frame_ID>_CENTER = 499
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'EULER'
FRAME_<frame_ID>_EPOCH = @2000-JAN-1/12:00:00
FRAME_<frame_ID>_AXES = ( 3 1 3 )
FRAME_<frame_ID>_UNITS = 'DEGREES'
FRAME_<frame_ID>_ANGLE_1_COEFFS = ( -47.68143 0.33621061170684714E-10 )
FRAME_<frame_ID>_ANGLE_2_COEFFS = ( -37.1135 -0.19298045478743630E-10 )
FRAME_<frame_ID>_ANGLE_3_COEFFS = ( -176.630 -0.40612497946759260E-02 )
Dynamic Frames 44
N IF Frozen Dynamic Frames - 1
Navigation and Ancillary Information Facility
• A frozen dynamic frame is a "Snapshot" of a
dynamic frame at a specified epoch.
– The frame is frozen relative to the base frame specified by
the frame kernel creator in the frame kernel definition.
– The rotation from the frozen frame to the base frame is
constant.
– The rotation is not frozen with respect to inertial frames
unless the base frame is inertial.
– A frame is designated frozen by the presence of a "freeze
epoch" specification in the frame definition, for example:
FRAME_<FRAME_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901
– The freeze epoch is given in SPICE text kernel format, as is
used in a leapseconds kernel.
Dynamic Frames 45
N IF Frozen Dynamic Frames - 2
Navigation and Ancillary Information Facility
Frozen version of Earth mean equator and equinox of date frame:
+Z axis is perpendicular to mean equator of date.
+X axis is parallel to cross product of +Z axis and
vector normal to mean ecliptic of date.
+Y axis completes the right-handed frame.
\begindata
<frame_name> = user-specified
FRAME_<frame_name> = <frame_ID> frame name
FRAME_<frame_ID>_NAME = <frame_name> <frame_ID> = integer frame ID
FRAME_<frame_ID>_CLASS = 5 code
FRAME_<frame_ID>_CLASS_ID = <frame_ID>
FRAME_<frame_ID>_CENTER = 399
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE'
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
FRAME_<frame_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901
Dynamic Frames 46
N IF Inertial Dynamic Frames - 1
Navigation and Ancillary Information Facility
• Inertial dynamic frames are specified by
setting the rotation state to 'INERTIAL' in
the rotation state assignment:
FRAME_<FRAME_ID>_ROTATION_STATE = 'INERTIAL'
– The 'INERTIAL' state implies the frame is treated as
inertial for the purpose of velocity transformations.
– The state transformation between any inertial frame and
"inertial dynamic frame" has zero derivative block: the
state transformation matrix has the form
R(t) | 0
-------|------
0 | R(t)
where R(t) is a time-dependent rotation.
Dynamic Frames 47
N IF Inertial Dynamic Frames - 2
Navigation and Ancillary Information Facility
– In contrast, for any rotating frame R(t), the state
transformation between any inertial frame and R(t) has a
corresponding matrix of the form
R(t) | 0
-------|------
dR(t)/dt| R(t)
– The inertial rotation state
» Simplifies velocity transformations: velocities are
transformed by a rotation.
» May be useful for maintaining consistency with other
dynamic frame implementations.
» Only makes sense if the "inertial" dynamic frame
actually rotates very slowly!
Dynamic Frames 48
N IF Inertial Dynamic Frames - 3
Navigation and Ancillary Information Facility
Inertial version of Earth true equator and equinox of date frame:
+Z axis is perpendicular to true equator of date.
+X axis is parallel to cross product of +Z axis and
vector normal to mean ecliptic of date.
+Y axis completes the right-handed frame.
\begindata
<frame_name> = user-specified
FRAME_<frame_name> = <frame_ID> frame name
FRAME_<frame_ID>_NAME = <frame_name> <frame_ID> = integer frame ID
FRAME_<frame_ID>_CLASS = 5 code
FRAME_<frame_ID>_CLASS_ID = <frame_ID>
FRAME_<frame_ID>_CENTER = 399
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE'
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976'
FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980'
FRAME_<frame_ID>_ROTATION_STATE = 'INERTIAL'
Dynamic Frames 49
N IF Generic Dynamic Frames Kernel
Navigation and Ancillary Information Facility
• NAIF is developing a "generic" dynamic
frames kernel.
– Will contain widely applicable dynamic frame
definitions.
– Analogous to generic PCK file.
– Examples of included frames:
» GSE, GSE, MAG
» Earth mean equator and equinox of date, 1976
version
» Earth mean equator and equinox of date, 1980
version
Dynamic Frames 50
N IF Backup
Navigation and Ancillary Information Facility
• Rationale
• Numerical Issues
• Limitations
Dynamic Frames 51
N IF Rationale
Navigation and Ancillary Information Facility
• Why provide dynamic frames?
– User could build C-kernel for *any* frame.
– SPICE could provide a limited number of "built-in" dynamic
frames which wouldn't require a frame kernel.
– Users can (and do) create their own routines to implement
dynamic frames.
• Benefits
– Convenience: using a formula rather than a C-kernel
avoids C-kernel creation, dissemination, storage, and
consistency issues
– Flexibility: the dynamic frame mechanism enables creation
of a vast variety of reference frames
– Integration: once defined, and once supporting kernels are
loaded, dynamic frames may be referenced in SPICE API
calls.
Dynamic Frames 52
N IF Numerical Issues - 1
Navigation and Ancillary Information Facility
• Two-vector frame derivatives may be inaccurate.
Let R(t) represent a time-dependent rotation:
– If R(t) depends on CK data, dR(t)/dt may be inaccurate because
CK rates frequently have low accuracy.
– If R(t) depends on velocity vectors, then dR(t)/dt depends on
acceleration determined via numerical differentiation. Typically
such derivatives suffer loss of accuracy.
» However, if velocities are "well-behaved," numerically derived
acceleration can be quite good. Example: GSE frame.
– If R(t) depends on position vectors, the velocities associated with
those vectors by the SPK system may not be mathematically
consistent with the positions. This can happen for SPK types
with separate polynomials for position and velocity, such as
types 3, 8, 9, and 14.
– If R(t) depends on aberration-corrected vectors, the associated
velocities may be inaccurate due to accuracy limitations of the
aberration corrections applied to velocities by the SPK system.
Dynamic Frames 53
N IF Numerical Issues - 2
Navigation and Ancillary Information Facility
• Recommendations
– Avoid using aberration corrections in two-vector frame
definitions, if accurate velocity transformations are required.
– Be aware of the accuracy of the data on which two-vector frames
are based.
Dynamic Frames 54
N IF Limitations - 1
Navigation and Ancillary Information Facility
• Simulated recursion:
– ANSI Fortran 77 doesn't support recursion, so the SPICE dynamic
frame system implements limited, simulated recursion.
» Basically, two levels of recursion are supported for selected
SPK and Frame System routines.
– Users must avoid requesting "deeper" recursion than the SPICE
dynamic frame system can support.
» When defining dynamic frames:
• Choose J2000 as the base frame for two-vector frames.
• Except for Euler frames, avoid using dynamic frames as base
frames.
• Try to avoid choosing a dynamic frame as the frame associated
with a velocity or constant vector.
» In SPK, CK, or PCK kernels, don't use two-vector frames as
the base frame relative to which ephemeris or attitude data
are specified.
• "Of-date" or Euler frames are OK for this purpose.
Dynamic Frames 55
N IF Limitations - 2
Navigation and Ancillary Information Facility
• Run-time efficiency:
– Dynamic frame evaluation typically requires more computation
than is needed for CK or PCK frames.
» For example, evaluation of a two-vector frame may involve
several SPK calls.
» Euler frames are an exception: these are fairly efficient as
long as they don't have a base frame that requires a lot of
computation to evaluate.
– To minimize the performance penalty:
» Use J2000 as the base frame for two-vector frames.
» Use the simplest frames possible for association with
velocity or constant vectors in two-vector frame definitions.
• Prefer non-dynamic frames to dynamic frames and inertial
frames to non-inertial frames where there is a choice.
Dynamic Frames 56
